Relativistic spinless particles in the generalized asymmetric Woods-Saxon potential

In this study, the Klein-Gordon equation in one spatial dimension is solved exactly for the generalized asymmetric Woods-Saxon potential containing the various forms of physical potentials, such as the usual Woods-Saxon, asymmetric Hulthen, usual Hulthen, asymmetric cusp and usual cusp potentials. The solutions that describe the scattering and bound states of the Klein-Gordon particles are obtained in terms of the hypergeometric functions. Using the boundary conditions satisfied by the wave functions and considering the asymptotic behavior of the wave functions, we examine a condition for the transmission resonances of the relativistic spinless particles in view of the generalized asymmetric Woods-Saxon potential. Furthermore, dependence of the transmission coefficients on the generalized asymmetric Woods-Saxon potential parameters as well as the energies of Klein-Gordon particles is investigated numerically by using the Mathematica Software.